This Youtube video depicts a Sami woman castrating a reindeer by biting off the testicles (although the moment suprême is not shown explicitly): Laplander Reindeer Castration (warning: video depicts animal suffering, and could be not safe for work unless you work in an abattoir). The video description states it is a Traditional Laplander reindeer castration from a film on the Laplander reindeer herding ritual.
I found a textual description in the book People of eight seasons: The story of the Lapps, by Ernst Mankel, Nordbok AB, 1975:
And the stranger who has accompanied the sita through thick and thin thinks that what is happening now looks more barbaric than any ancient historian could depict it — the manner, that is, not the actual principle, which in ancient times was practiced on many a male child. The great, tough animal lies helpless on its back or side with its head pressed against the earth and held fast by the herdsman's foot on the front branches of the antlers and a firm grip on the long main branches — levers in the herdsman's hands to counteract the strength in the animal's neck. While one man thus holds the bull fast, another — the operator — gets down on his knees behind it and puts his hands and head between its back legs, grasps the testicles firmly between his fingers and — bites, first one, and then the other. They snip off like a large gooseberry or a plum, one snip each and then the pouch is massaged a little. And a härk, an ox, is released and trots off to the other animals."
The skeptic that I am, I searched on. I couldn't find anything related to reindeer, but I found this Google Answers thread about sheep, which states (with sources) that shepherds do hold the testicles with their teeth, but then use a knife to cut off the testicles:
They would hold the testicles tight underneath, slit the skin holding the testicle in, put their mouth down and get hold of the testicle with their teeth, lift it up a bit, slice it off with the knife in their other hand and then spit the testicle on the ground.
I doubt it was done differently, as in literally biting them off without the aid of a knife, since a human's teeth are not nearly adequate enough to make that kind quick amputation necessary to keep from crippling an animal or preventing it from bleeding to death before the task was completed (not to mention the enormous infection and mortality rate this would have created).
In summary, it does appear that some farm animal castrations were "teeth assisted", if that makes sense, but quite unlikely, for obvious reasons, dependent upon human teeth alone
Finally, the Google Answers link is inconclusive, as are other sources I have been able to find online. Sheep are not reindeer, although I would be surprised if a reindeer's testicles are easier to bite off than a sheep ones.
Is it possible for a human to bite off a reindeer's testicles?